Concrete is the most widely used building material in the world. There are many types of concrete, each is created by varying portions of cement, water, aggregate and chemical admixtures. Through a process called mineral hydration, the cement bonds the other components together and forms a rock like structure known as concrete. The reaction between cement and water is highly exothermic so if the hydration process occurs too quickly the concrete will not form strong bonds. It is desirable to slow down the reaction by cooling so the structure of the concrete will not be compromised.
It is especially difficult to cool concrete in large structures like dams. Dams are constructed by pouring large concrete slabs (e.g. 10 m x 10 m x 3 m) that can take many years to cool due to the low rate of thermal conductivity coupled with the highly exothermic reaction of water and cement. Large temperature differences within the concrete causes the concrete to form stress cracks that weaken the structure. Ideally, the core temperature of the concrete slab should be no more than 24oC greater than the surface temperature, but if left unattended the difference can be over 50oC. To reduce the build up of temperature during the curing process, cold water travel thorough a network of pipes embedded in the concrete. This process takes about 28 days and once complete, the pipes are filled in with concrete.
The following steps need to be determined to achieve a cost effective way to cool the concrete:
- the optimal pipe radius
- the optimal pipe length
- temperature and flux of water through the pipes
- spacing and geometric arrangement of pipes in the water network
What are Rates of Change?
A Simple Example of the Optimization of a Cylinder
How to Find the Optimal Pipe Radius
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